Spatial-temporal data.

Napoleon's march on Moscow - C. J. Minard (1781-1870)

Tufte "It may be the best statistical graphic ever drawn."

There are 6 variables: army size

location (2)

direction of movement (2)

temperature

thickness: army size, retreat: dark band

movements of auxiliary troops

Spatial-temporal field.

Y(x,y,t): 0 x X-1, 0 y Y-1, 0 t T-1

Y(r,t)

1200 GMT, 1 Jan 86, every 12 hrs

data 5300m and below dashed linee

speed and direction of moving depression?

Aggregated regional data.

Yj (t): j census division - vertices given

t time - 1986, 1987

Array data

Y(xj , yj ,t), j=1,...,J Y(rj ,t) rj = (xj , yj )

Often for measuring direction and speed

SMART 1 array in Taiwan

seismomenters in concentric circles, picked 9 here

data 3D - x-, y-, z- components

noise in buffer

epicenter 30km SE

P wave

EEG data. W. Freeman

evoked response

8 by 8 array of sensors

studying outside row - a linear array (oceanography)

Y(x,t) 0 x X-1 0 t T-1

contour and image displays

Death counts and rates

Y(x,t): t year, x age

linear array

circle radius ~ count or rate

symbols()

Moving particles, trajectories. motility

r(t) = (x(t),y(t)), t = 0, 1, ..., T-1

Y(x,y,t) = (x-x(t),y-y(t))

Y(r,t) = (r - r(t)) r = (x,y)

"Brownian" motion

Perrin (1913) Guttorp book

microtubules

Elephant seal

Moving particle in 3 D

ringed seal Barrow Strait, NWT

position estimated by an array of 5 sensors

r = (x,y,z)

Y(r,t) = (r - r(t))

r(t) = (x(t),y(t),z(t))

Adding depth to X-Y trajectory

losing identifiability

Munk seal, endangered species

Molokai

OZ

Elk. Starkey Reserve. Case with explanatory x(t)

Can elk, deer, cows, humans coexist?

Moving cells.

chicken embryo

described by polygons, Pj (t)

part of tesselation

Separation of variables

Look at Y(x,y), Z(t) separately

Daily births in Saskatchewan